Tagged Questions

Factorization is the problem of taking an integer and finding the set of prime numbers that produce the integer when multiplied together. For large integers with large factors, factorization is hard and is the basis for cryptosystems like RSA.

The two primes $p$ and $q$ part of the public key need to be distinct.
What's the reason for them to be distinct? Is it because factorization of $p^2$ where $p$ is a prime is relatively easier, or is ...

I am facing a challenge at university.
Our teacher give us the challenge to try to break an RSA 1024 bit.
We have public modulus N and public exponent e (0x03), we don't know the padding.
We have a ...

It is given two RSA moduli $N_1$ and $N_2$, known to be of the form $N_i=p_i\cdot q_i$, with $p_i$ and $q_i$ unknown primes, and such that $p_2=p_1+2$. Can we make use of that relation to factor the ...

Here I overconfident in myself state that I can show, that n has two factors.
This is not completely true, can possibly show $n$ is composite - prover generates RSA key with modulo $n$, and gives $e$ ...

I was reading about the Blum-Blum-Shub random number generator, and its security depends on the hardness of factoring very large numbers (like many things in crypto do).
I'm just wondering, if I have ...

Given an integer you want to factor $N$, GNFS starts by selecting a monic irreducible polynomial $f \in \mathbb{Z}[X]$ and an integer $m$ such that $f(m) \equiv 0 \text{ mod } N$. In practice, if $m$ ...

In the article A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any ...

In the article "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems", the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any ...

I came across these questions while studying for a crypto course, does anyone have any ideas on how to answer these?
(a) Random prime numbers of size 1536 bits are chosen to generate
an RSA modulus ...

Given the RSA modulus $N$ the fastest method to factor it is of sub-exponent order. But, now if I know the private key $d$ of RSA, does that mean I can factor $N$ efficiently?. It intuitively seems ...

Factoring some 20-45 digit values n with a (simple) quadratic sieve, the quadratic sieve may end up with pairs of x and y s.t. $x^2 \equiv y^2 \pmod n$, but neither x+y nor x-y has a nontrivial gcd ...

I understand how ECC is based on the discrete log problem and RSA on integer factorization. I've read several references that show how a solution to either of these problems can typically be adapted ...

I'm looking around for publicly published work on factorization of large numbers using distributed systems of any kind. So far I've come across the PDF "Mapreduce for integer factorization" by Javier ...

Currently I'm working on a presentation of a paper that talks about the factorization of large numbers. In the paper elliptic curves are presented as a way to factorize large numbers. After hearing a ...

I am trying to factor few integers that are each between 115 and 135 digits long. I was wondering if anyone knew of any efficient methods or any programs that I could use to find the two primes $p$ ...

It seems to me an exhaustive search would simply try to use all the possible bit combinations of a key, while factorization is some mathematical formula for determining the key? When discussing the ...

I cannot seem to understand the role or goal of Quantum Fourier Transformation in Shor's integer factorization algorithm. Is it used to collapse all quantum states into one, in which it has a factor ...

I am researching vulnerable RSA moduli which are composed of primes generated with poor entropy. Having a list of these primes I searched for variable sized repeated patterns among them and I noticed ...

I am using an algorithm (can be found here1) that can compute efficiently the GCD of multiple RSA keys. It intended for RSA keys that were generated with low entropy and may have one of their primes ...

I am trying to look into a relation between the following three problems which are widely used to build public crypto systems:
Integer Discrete log
Elliptic Curve Discrete log
Integer Factorization
...

I am a bit confused on the hardness of the discrete logarithm problem. Does it become intractale only when it is mod n, where n is a large composite number (Like RSA key). What about if it is mod a ...

In 2012 a group of researchers collected a large amount of RSA moduli and calculated their greatest common divisor in order to find common factors between them. By finding a common factor they could ...

There is a paper from Peter W. Shor from 1994: http://www.csee.wvu.edu/~xinl/library/papers/comp/shor_focs1994.pdf "Algorithms for Quantum Computation: Discrete Logarithms and Factoring", and I have a ...

Suppose you got a prime $p = 2\mathbb\Pi_{i=0}^{n-1}q_i+1$, where $2^{k-1} \lt q_i \lt 2^k$ for some $k$ and all $0 \le i \lt n$, and that you also got a generator $g$ of one of the prime order sub ...